The United States and Japan will step up their defence cooperation to deal with the threat from nuclear-armed North Korea as tensions in East Asia remain high, officials from the two allies said on Thursday.

Police have continued their search for the body of NSW teacher Sharon Edwards, who went missing more than two years ago, at the home of her estranged husband after he was charged with her alleged murder.

Excavations entered a third day around 9am this morning in the backyard of John Edwards’ property in Lawrence, north of Grafton.

The renewed search continues after Mr Edwards, 61, was extradited to NSW and charged with the alleged murder of his former wife yesterday.

He has been refused bail.

Ms Edwards, 55, was last seen alive by her husband at their Lawrence home in March 2015.

Two weeks after her disappearance, Mr Edwards took to television to issue an impassioned plea for information regarding his wife's whereabouts.

Her body has never been recovered but police treated her disappearance as a homicide, and her husband was considered a suspect.